Recurrence Relations

  • George E. Martin
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

A recurrence relation for a sequence {a i }, which usually begins with a 0 or a 1, is a formula that defines a n in terms of a 0, a 1, a 2, a 3,..., a n−1, and n for all n greater than some particular integer k, with the terms a 0, a 1,..., a k called initial conditions or boundary conditions. Together with the initial conditions, the recurrence relation provides a recursive definition for the elements of the sequence. This allows us to compute the unique value of a n for each integer n such that n > k. Many examples follow. We are already familiar with several recurrence relations.

Keywords

Recurrence Relation Binary Sequence Fibonacci Sequence Catalan Number Quaternary Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • George E. Martin
    • 1
  1. 1.Department of Mathematics and StatisticsState University of New York at AlbanyAlbanyUSA

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